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Tomo Munehisa

Publications and source records attributed to Tomo Munehisa.

16 recordsLinked to original sources
arXiv2024

Violation of Cluster Property in Superconducting Qubit

Spontaneous symmetry breaking is well known to be a macroscopic phenomenon in quantum physics in many body systems. The essential features of this phenomenon are the energy degeneracy and the existence of the local operator that can modify the degenerate states. Due to these properties the lowest energy state is not stable. In order to obtain the stable ground state we introduce the explicitly breaking interaction, by which it is difficult for the local operator to modify the ground state. In the superconducting qubit there exists the stable eigenstate with the definite charge number. We point out that in this system, the local operator can change this state to another state. As results the cluster property violates, which means that the events in the far distance are not irrelevant. In this paper we examine the cluster property in the superconducting qubit. Then we propose a method by cavity quantum electrodynamics with two cavities in order to observe the violation.

cond-mat.stat-mech↗
arXiv2013

Numerical Study on Spontaneous Symmetry Breaking in a XY Quantum Antiferromagnet on a Finite Triangular Lattice

Motivated by recent experiments that require more complicated macroscopic wave functions in the condensed matters, we make numerical study on a XY quantum antiferromagnet on a finite triangular lattice using the variational Monte Carlo method and the stochastic state selection method. One of our purpose is a numerical confirmation on dominance of a Nambu-Goldstone boson in low energy excitation. For another purpose, we calculate energy, an expectation value of a symmetry breaking operator and structure functions of spin by fixing a quantum number of the symmetry. These calculations are made for states that become degenerate in an infinitely large lattice. By numerical calculations we confirm existence of a Nambu-Goldstone boson, and find dependence of a square of the quantum number for the above quantities. Using these results we can discuss on complicated macroscopic wave functions in quantum spin systems.

cond-mat.stat-mech↗
arXiv2010

Numerical study of the spin-1/2 Heisenberg antiferromagnet on a 48-site triangular lattice

We numerically study the magnetization and the dispersion relation of a frustrated quantum spin system. Our method, which is named the stochastic state selection method, is a kind of Monte Carlo method to give eigenstates of the system through statistical averaging processes. Using the stochastic state selection method with some constraints, we make a successful study of the spin-1/2 Heisenberg antiferromagnet on a 48-site triangular lattice. We calculate the sublattice magnetization and the static structure function in the ground state. Our result on the sublattice magnetization is consistent with the value given by the linear spin wave theory. This adds an evidence for the analysis based on the spontaneous symmetry breaking of the semi-classical Neel order in the ground state. We also evaluate the low-lying one magnon spectra of the model with all wave vectors available on a 48-site triangular lattice. We find that at the ordering wave vector there is a Goldstone mode, which is in good agreement with the result from the spin wave analysis. The magnon spectra with other wave vectors, however, are quite different from results obtained by the linear spin wave theory. We observe a flat dispersion relation with a strong downward renormalization. Our results are compatible with those recently reported in the series expansion study and in the order 1/S calculation of the spin wave analysis.

cond-mat.stat-mech↗
arXiv2009

A constrained stochastic state selection method applied to quantum spin systems

We describe a further development of the stochastic state selection method, which is a kind of Monte Carlo method we have proposed in order to numerically study large quantum spin systems. In the stochastic state selection method we make a sampling which is simultaneous for many states. This feature enables us to modify the method so that a number of given constraints are satisfied in each sampling. In this paper we discuss this modified stochastic state selection method that will be called the constrained stochastic state selection method in distinction from the previously proposed one (the conventional stochastic state selection method) in this paper. We argue that in virtue of the constrained sampling some quantities obtained in each sampling become more reliable, i.e. their statistical fluctuations are less than those from the conventional stochastic state selection method. In numerical calculations of the spin-1/2 quantum Heisenberg antiferromagnet on a 36-site triangular lattice we explicitly show that data errors in our estimation of the ground state energy are reduced. Then we successfully evaluate several low-lying energy eigenvalues of the model on a 48-site lattice. Our results support that this system can be described by the theory based on the spontaneous symmetry breaking in the semiclassical Neel ordered antiferromagnet.

cond-mat.stat-mech↗
arXiv2007

An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method

We develop a new method to calculate eigenvalues in frustrated quantum spin models. It is based on the stochastic state selection (SSS) method, which is an unconventional Monte Carlo technique we have investigated in recent years. We observe that a kind of equilibrium is realized under some conditions when we repeatedly operate a Hamiltonian and a random choice operator, which is defined by stochastic variables in the SSS method, to a trial state. In this equilibrium, which we call the SSS equilibrium, we can evaluate the lowest eigenvalue of the Hamiltonian using the statistical average of the normalization factor of the generated state. The SSS equilibrium itself has been already observed in un-frustrated models. Our study in this paper shows that we can also see the equilibrium in frustrated models, with some restriction on values of a parameter introduced in the SSS method. As a concrete example, we employ the spin-1/2 frustrated J1-J2 Heisenberg model on the square lattice. We present numerical results on the 20-, 32-, 36-site systems, which demonstrate that statistical averages of the normalization factors reproduce the known exact eigenvalue in good precision. Finally we apply the method to the 40-site system. Then we obtain the value of the lowest energy eigenvalue with an error less than 0.2%.

cond-mat.stat-mech↗
arXiv2006

The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems

We describe a further development of the stochastic state selection method, a new Monte Carlo method we have proposed recently to make numerical calculations in large quantum spin systems. Making recursive use of the stochastic state selection technique in the Lanczos approach, we estimate the ground state energy of the spin-1/2 quantum Heisenberg antiferromagnet on a 48-site triangular lattice. Our result for the upper bound of the ground state energy is -0.1833 +/- 0.0003 per bond. This value, being compatible with values from other work, indicates that our method is efficient in calculating energy eigenvalues of frustrated quantum spin systems on large lattices.

cond-mat.str-el↗
arXiv2004

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.

cond-mat.stat-mech↗
arXiv2004

Numerical Study for an Equilibrium in the Recursive Stochastic State Selection Method

We apply the recursive stochastic state selection method, which is a new method for Monte Carlo study we have recently developed, to quantum spin systems with positive definite Hamiltonians. Through numerical studies of two-dimensional J1-J2 Heisenberg model on a square lattice with unfrustrated couplings J1=1 and J2=-1 and with non-frustrated ones J1=1 and J2=0, we find that a kind of equilibrium is realized in these systems. We also observe that in this equilibrium we can obtain a quite accurate estimate of the energy eigenvalue for the system's ground state. Statistical relative errors in our results are 0.03% for the 36-site unfrustrated model and 0.06% for the 64-site non-frustrated model.

cond-mat.str-el↗
arXiv2004

The Stochastic State Selection Method for Energy Eigenvalues in the Shastry-Sutherland Model

We apply a recently developed stochastic method to the Shastry-Sutherland model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State Selection Method here, enables us to evaluate expectation values of powers of the Hamiltonian with very limited number of states. In this paper we first apply it to the 4x4 Shastry-Sutherland system, where one can easily obtain the exact ground state, in order to demonstrate that the method works well for this frustrated system. We numerically show that errors of the evaluations depend much on representations of the states and that the restructured representation is better than the normal one for this model. Then we study the 8x8 system to estimate energy eigenvalues of the lowest S=1 state as well as of the lowest excited S=0 state, where S denotes the total spin of the system. The results, which are in good accordance with our previous data obtained by the Operator Variational method, support that an intermediate spin-gap phase exists between the singlet dimer phase and the magnetically ordered phase. Estimates of the critical coupling and of the spin gap for the transition from the dimer phase to the intermediate phase are also presented.

cond-mat.stat-mech↗
arXiv2003

A New Approach to Stochastic State selections in Quantum Spin Systems

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of the Hamiltonian from a small portion of the full vector space. This method is free from the negative sign problem because it is not based on importance sampling techniques. In this paper we describe our method and, in order to examine how effective it is, present numerical results on the 4x4, 6x6 and 8x8 Heisenberg spin one-half model. The results indicate that we can perform useful evaluations with limited computer resources. An attempt to estimate the lowest energy eigenvalue is also stated.

cond-mat.str-el↗
arXiv2002

Numerical Study of Excited States in the Shastry-Sutherland Model

We investigate excited states of the Shastry-Sutherland model using a kind of variational method. Starting from various trial states which include one or two triplet dimers, we numerically pursue the best evaluation of the energy for each set of quantum numbers. We present the energy difference as a function of either the coupling ratio or the momentum and compare them with the perturbative calculations. Our data suggest that the helical order phase exists between the singlet dimer phase and the magnetically ordered phase. In comparison with the experimental data we can estimate the intra-dimer coupling J and the inter-dimer coupling J' for SrCu2(BO3)2 : J'/J =0.65 and J = 87K.

cond-mat.str-el↗
arXiv1997

Quantum Monte Carlo Study of an Extended Hubbard Model on a Two-leg Ladder

An extended Hubbard model on a two-leg ladder is numerically studied by means of the quantum Monte Carlo techniques. The model we study has the nearest-neighbor interactions which are repulsive along chains and attractive for rungs. The plots of the doping parameter versus the chemical potential show two cliff-like regions and a large plateau region. Results on the charge susceptibility suggest it diverges in these cliff-like regions. These observations might imply a signal to the phase separation, which should be related to the effective attractive interactions along chains.

cond-mat.str-el↗
arXiv1995

Study on Ground States of Quantum Spin Systems by Restructuring Method

We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the expansion of the ground state from measurements of the normalized frequencies of each state on the boundary in the Trotter direction. The restructuring method we have proposed makes it possible to carry out simulations within available resources of computers. For a concrete example we study ladder spin systems with antiferromagnetic intra-chain nearest neighbor interactions, whose ground states may be equivalent to that of the spin 1 chain. For the ladder with ferromagnetic rungs we successfully show how to determine the magnitudes and relative signs of the coefficients in the expansion. When the ladder has antiferromagnetic rungs we examine White's claim that the diagonally situated pair of spins are mostly triplet states in the ground state. Our results strongly suggest that the system has the hidden order which is constructed by the specially aligned triplet states of diagonal pairs.

cond-mat↗
arXiv1994

A Hybrid Method for Global Updates in Monte Carlo Study

We propose a new algorithm which works effectively in global updates in Monte Carlo study. We apply it to the quantum spin chain with next-nearest-neighbor interactions. We observe that Monte Carlo results are in excellent agreement with numerically exact ones obtained by the transfer matrix method.

cond-mat↗
arXiv1994

Re-Structuring Method for the Negative Sign Problem in Quantum Spin Systems

We present detailed discussions on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states in the path integral formulation. We observed our approach brings remarkable improvement in the negative sign problem when applied to one-dimensional quantum spin $1/2$ system with next-to-nearest neighbor interactions. In this paper we add some descriptions on our method and show results from analyses by the exact diagonalization and by the transfer matrix method of the system on a small chain. These results also indicate that our method works quite effectively.

cond-mat↗